Question

A person deposits $100 at the beginning of each year for 20 years. Simple interest at an annual rate of i is credited to each deposit from the date of deposit to the end of the twenty year period. The total amount thus accumulated is $2840. If instead, compound interest had been credited at an effective annual rate of i, what would the accumulated value of these deposits have been at the end of 20 years

Answer 1

Future value if compounding interest: $3,096.9202

Step-by-step explanation:

The simple interest do not consider that interest generate more interest like compounding. It considers the investor withdraw their return rather than reinvesting.

`FV = PMT * time \left[1+rate *(time + 1 )/(2) \right]`

100 x 20 x (1 + i x (20+1)/2) = 2,840

(2,840/2,000 -1) x 2 / 21

r = 0.04

Now, we solve considering compounding which assume all interest are reinvested.

`C * ((1+r)^(time) -1)/(rate)(1+r) = FV\\`

C 100.00

time 20

rate 0.04

`100 * ((1+0.04)^(20) -1)/(0.04)(1+0.04) = FV\\`

FV $3,096.9202